Context. Finding low-mass planets around solar-type stars requires understanding the physical variability of the host star, which greatly exceeds the planet-induced radial-velocity modulation. Different solar photospheric absorption lines have slightly disparate responses to stellar activity, which should permit us to disentangle the wavelength shifts induced by exoplanets from those originating in stellar atmospheres. Aims. Changing area coverages of magnetic active-region granulation (faculae and plage) cause radial-velocity fluctuations of the disk-integrated solar spectrum, whose precise modeling requires active-region spectral line profiles. Hydrodynamic 3D modeling of granulation in magnetic fields extends previous nonmagnetic studies, revealing different line profiles and altered convective velocity shifts. Methods. Different types of lines in the visual and near-infrared are examined in synthetic hyper-high-resolution spectra (λ/∆λ ~900 000), comparing nonmagnetic areas with those with strongly magnetic (240 mT = 2400 G) granulation. Results. Magnetic fields inhibit convective motions, decrease the energy flow, produce more symmetric lines, and remove the common blueshift with its familiar C-shaped bisectors. Unexpectedly, magnetic granulation displays convective redshifts. Their origin is traced to contributions from small areas, where hot and bright down-moving elements are created through shocks and adiabatic compression when rising gas is forced over into magnetically channeled downflows. Conclusions. Understanding line formation in also stellar active regions is needed to simulate full-disk spectra toward exoEarth detections. Detailed shapes of spectral lines carry significant information, suggesting that hyper-high spectral resolution may ultimately be required.